# Chapter 6 - Section 6.1 - Rational Functions and Multiplying and Dividing Rational Expressions - Exercise Set: 36

$\dfrac{a-5b}{a^{2}+ab}\cdot\dfrac{b^{2}-a^{2}}{10b-2a}=\dfrac{a-b}{2a}$

#### Work Step by Step

$\dfrac{a-5b}{a^{2}+ab}\cdot\dfrac{b^{2}-a^{2}}{10b-2a}$ Factor both rational expressions completely: $\dfrac{a-5b}{a^{2}+ab}\cdot\dfrac{b^{2}-a^{2}}{10b-2a}=\dfrac{a-5b}{a(a+b)}\cdot\dfrac{(b-a)(b+a)}{2(5b-a)}=...$ Evaluate the product: $...=\dfrac{(a-5b)(b-a)(a+b)}{2a(a+b)(5b-a)}=...$ Change the sign of the numerator and the denominator: $...=\dfrac{-(a-5b)(b-a)(a+b)}{-2a(a+b)(5b-a)}=\dfrac{(a-5b)(a-b)(a+b)}{2a(a+b)(a-5b)}=...$ Simplify by removing the factors that appear both in the numerator and in the denominator: $...=\dfrac{a-b}{2a}$

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